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We show that quantum game theory offers solution to the famous Newcomb's paradox (free will problem). Divine foreknowledge is not necessary for successful completion of the game because quantum theory offers a way to discern human…

Over the last twenty years of research on quantum game theory have given us many ideas of how quantum games could be played. One of the most prominent ideas in the field is a model of quantum playing a 2x2 game introduced by J. Eisert, M.…

Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The authors have recently proposed a quantum description of financial market in terms of quantum game…

According to the Gottesman-Knill theorem, quantum algorithms which utilise only the operations belonging to a certain restricted set are efficiently simulable classically. Since some of the operations in this set generate entangled states,…

This paper considers the decidability of fully quantum nonlocal games with noisy maximally entangled states. Fully quantum nonlocal games are a generalization of nonlocal games, where both questions and answers are quantum and the referee…

In a recent paper, Eisert et al. presented a quantum mechanical generalization of Prisoner's Dilemma. They asserted that the maximally entangled game exhibits a unique Nash equilibrium which yields a pay-off equivalent to cooperative…

Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…

Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration problem, for which a speed-up is shown by quantum computers…

We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players…

The computational study of equilibria involving constraints on players' strategies has been largely neglected. However, in real-world applications, players are usually subject to constraints ruling out the feasibility of some of their…

Quantum computers (QCs) are maturing. When QCs are powerful enough, they may be able to handle problems in chemistry, physics, and finance that are not classically solvable. However, the applicability of quantum algorithms to speed up…

I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine that, thanks to a many body interaction, reversibly and nondeterministically produces the solution of the problem…

We propose a concept of quantum extensive-form games, which is a quantum extension of classical extensive-form games. Extensive-form games is a general concept of games such as Go, Shogi, and chess, which have triggered the recent AI…

Optimal control theory is a promising candidate for a drastic improvement of the performance of quantum information tasks. We explore its ultimate limit in paradigmatic cases, and demonstrate that it coincides with the maximum speed limit…

We investigate quantum strategy in moving frames by considering Prisoner's Dilemma and propose four thresholds of $\gamma$ for two players to determine their \textit{Nash Equilibria}. Specially, an interesting phenomenon appears in…

Machine learning is frequently listed among the most promising applications for quantum computing. This is in fact a curious choice: Today's machine learning algorithms are notoriously powerful in practice, but remain theoretically…

We propose a simple yet rich model to extend the notions of Nash equilibria and correlated equilibria of strategic games to the quantum setting, in which we then study the relations between classical and quantum equilibria. Unlike the…

The core of quantum machine learning is to devise quantum models with good trainability and low generalization error bound than their classical counterparts to ensure better reliability and interpretability. Recent studies confirmed that…

Genetic algorithms are heuristic optimization techniques inspired by Darwinian evolution. Quantum computation is a new computational paradigm which exploits quantum resources to speed up information processing tasks. Therefore, it is…

The two-players $N$ strategies games quantized according to the Eisert-Lewenstein-Wilkens scheme (Phys. Rev. Lett. 83 (1999), 3077) are considered. Group theoretical methods are applied to the problem of finding a general form of gate…